One can imagine that the Predictor, who is also a truth-teller it turns out, tells your buddy whether or not the million is in the box. What would your buddy, who has all the information about the potential payoffs, recommend that you do? If he had your financial interests at heart, he would always, no matter what the Predictor did, recommend you take two boxes. It would seem completely irrational to go against the advice of your well-informed buddy.

it was apparently orgininally formulated to point out problems with bayesian decision theory, and some people have argued that it's identical with the prisoner's dilemma. iow rather than a fun game for all to play it is more of a thing for philosophers to puzzle over and write lots of papers containing lines like "v(b1) = v(m).p(m/b1)+v(n).p(n/b1) = 990,000".

All that matters is that Bob is a reliable predictor, it doesn't matter how he does it - it could even be pure luck. That's really the point, in fact - the result is probabilistically dependent on what you pick (because of Bob's history of reliable predictions) - but causally independent (because Bob is only predicting, not affecting the outcome: the money is already in the boxes).

If the predictor isn't 100% accurate, then this isn't about free will. If the predictor is 100% accurate, then the problem of free will is implied, but not demonstrated by the problem itself. At best, this problem seems to be a good way to stimulate discussion about why the population is split on their decision-making strategies.

Btw, I think you have to take both boxes. Whatever he predicts, he isn't predicting anything at the moment that you're choosing a box. There's no reverse causality.

― Mordy, Tuesday, May 25, 2010 10:15 PM (Yesterday)

going to disagree with this, the whole question hinges on the idea that your choice creates the status of the boxes. this would be more clear if bob was 100% accurate, but even with the slight margin of error in your formulation, theres no point in taking the super long shot.

still say this isnt a paradox, but rather an uncomfortable counterfactual situation that irritates people because we are wired to be really defensive about free will, and reject reverse causation out of hand. within the structure of bob world, free will (in this case) is suspended, and reverse causation is possible by definition, which removes the paradox.

as counterintuitive as it seems on the surface, HI DERE is right about the flux aspect of the money because standard temporal rules are suspended in this case (again, this is even more obvious in the case of the 100% accurate bob). the money in the boxes is indeterminate until you make your choice, which again, i realize is a punch in the directional time part of the brain, but infallible predictors dont exist either so you get what you get.

Bob (almost) always predicts what you are going to do correctly, regardless of the mental contortions you go through in making your decision. If you decide to take both boxes, he will have predicted that you will take both boxes. If you take one, he will have predicted you will take one. You're betting on him being wrong, something he rarely is based on the setup, ergo by taking both boxes you are betting on the long odds that he has made a mistake, whereas if you take one, you are betting against the log odds that he has made a mistake.

If the predictor is less than 100% accurate, does your choice create the status of the boxes? The prediction creates the status of the boxes, but the predictor could be wrong about your choice. If the predictor is wrong, then your choice had nothing to do with the causality of the status of the boxes.

Here's a more realistic version of the problem, where the answer seems fairly clear (and it's the equivalent of two-boxing). (And it's nothing to do with free will.)

Though it is well established that there is a strong statistical correlation between smoking and lung cancer, it doesn't follow that smoking is a cause of cancer. The statistical association might be due to a common cause (a certain genetic pre-disposition say) of which smoking and lung cancer are independent probable effects. (This is sometimes referred to as "Fisher's smoking hypothesis"). If you have the bad gene you are more likely to get lung cancer than if you don't, and you are also more likely to find that you prefer smoking to abstaining. Suppose you are convinced of the truth of this common cause hypothesis and like to smoke. Does the fact that smoking increases the probability of lung cancer give you a reason not to smoke?

I don't think this problem has anything to do with free will. Probability is different than causality, right? The problem seems to be that the probability changes depending on your choice, given a reliable predictor.

i agree that this works out to be a probability thing because of the not 100%, but the supposed paradox is all about the idea that if the money is already in the boxes, you should always take both boxes vs. choosing one box because your box choosing creates the state of money in the boxes, which means that the paradox attempt here has everything to do with causation and nothing to do with probability.

The problem is intended to be about expected-utility principle vs. dominance principle, and it works if it creates a scenario wherein both principles are equally valid. If both principles are equally valid in this scenario and they both lead to different choices, then there is an apparent paradox.

I don't think the mechanism for the reliability of the predictor is important, because the chooser can't know how or why the predictor is reliable. He could be right because he is prescient. He could be right because he has a lot of information, and he's dropping science. He could have been calling heads or tails right, without any special knowledge, every time up until now.

Am I causing the boxes to be in a particular state by making a choice, or is the state of the boxes fixed before I make my decision? There is no evidence contained within the problem to make me choose one way or the other. The question is whether I accept that he is a reliable predictor.

Given that I do accept that he is a reliable predictor, do I apply the expected-utility principle, or the dominance principle? What is the most rational choice?

Am I causing the boxes to be in a particular state by making a choice, or is the state of the boxes fixed before I make my decision? There is no evidence contained within the problem to make me choose one way or the other.

Not as stated in this thread, but it is written into various formulations. Sometimes it's stated that Bob puts the money in the boxes e.g. an hour before you make your choice. Also the version where your friend knows what's in the boxes obviously requires the amount to be pre-determined.

I don't think the mechanism for the reliability of the predictor is important

True enough. It is far more important to know Bob's actual accuracy, which ought to be measurable more exactly than "almost always", than the mechanism of prediction. However, the mechanism is of interest in that it establishes what sort of universe we are inhabiting, and that allows us to judge whether Bob's methods are as likely to be accurate in the matter of boxes filled with cash as they are with other, past actions he has predicted.

BTW, Bob's would appear to be a magical universe, in that there is as yet no imaginable mechanism for predicting my actions in this universe with such near infallibility, without invoking magic, or a diety with magical propoerties. However, if this magical universe is inherently as predictable in as a lawful one, then the mechanism is of no importance, for they will act commensurately. IOW, the magical process must follow laws just as strict and as predictable as physical laws.

Am I causing the boxes to be in a particular state by making a choice, or is the state of the boxes fixed before I make my decision? There is no evidence contained within the problem to make me choose one way or the other.

Not as stated in this thread, but it is written into various formulations. Sometimes it's stated that Bob puts the money in the boxes e.g. an hour before you make your choice. Also the version where your friend knows what's in the boxes obviously requires the amount to be pre-determined.

If the predictor is prescient, then it doesn't matter when the cash goes in the box--it's still a matter of reverse-causality. I agree that the problem is basically bullshit if the thought-problem is about a being who is infallible.

It's just, if the friend has your best interests at heart and is telling you to take both boxes, then the friend is changing the parameters of the scenario and makes Bob's prediction null and void; the assumption becomes that Bob always puts the $100K into box B and you should always take both because your friend who is, by definition of the problem, not attempting to screw you over knows that the money in the boxes.

actually i dont see any case where the timing of when the cash goes in the box matters. i think what some people are missing is that reverse-causation doesn't imply that the money is actually literally in flux until the instant your decision is made, but functionally thats the only way to view it - the whole thing hangs on the inherent difficulty of prediction wrt linear time. the gap between when the prediction was made/when the cash was put in the box is immaterial really.

Having read the original formulation of the problem by Newcomb (link above), he glosses over the mechanism as irrelevant, and also glosses over what sorts of experience the person asked to make the choice has had with prior predictions, stating only that you know the being (aka Bob):

"has often correctly predicted your choices in the past (and has never so far as you know made an incorrect prediction about your choices) and furthermore this being has often correctly predicted the choices of other people, many of whom are similar to you, in the particular situation to be described below".

I especially like how he plays both sides of the street by saying that you do not know of any predictive errrors in your own case, but that you know (with equal emphasis) that the being's track record in this regard is only "often" correct. Which looks to me like a contradiction: either you know of some errors, or you don't know the being's record is only "often" correct. These can't both be true.

That sort of hand waving makes the problem suck as an exercise in logic or problem solving.